Thermodynamics

QH 2 O200 kPa200°CFIGURE P4–38Chapter 4 | 2054–42 A 30-L electrical radiator containing heating oil isplaced in a 50-m 3 room. Both the room and the oil inthe radiator are initially at 10°C. The radiator with a ratingof 1.8 kW is now turned on. At the same time, heat is lostfrom the room at an average rate of 0.35 kJ/s. After sometime, the average temperature is measured to be 20°C for theair in the room, and 50°C for the oil in the radiator. Takingthe density and the specific heat of the oil to be 950 kg/m 3and 2.2 kJ/kg °C, respectively, determine how long theheater is kept on. Assume the room is well-sealed so thatthere are no air leaks.4–39 Reconsider Prob. 4–38. Using EES (or other)software, investigate the effect of the initial temperatureof steam on the final temperature, the work done,and the total heat transfer. Let the initial temperature varyfrom 150 to 250°C. Plot the final results against the initialtemperature, and discuss the results.4–40 A piston–cylinder device initially contains 0.8 m 3 ofsaturated water vapor at 250 kPa. At this state, the piston isresting on a set of stops, and the mass of the piston is suchthat a pressure of 300 kPa is required to move it. Heat is nowslowly transferred to the steam until the volume doubles.Show the process on a P-v diagram with respect to saturationlines and determine (a) the final temperature, (b) the workdone during this process, and (c) the total heat transfer.Answers: (a) 662°C, (b) 240 kJ, (c) 1213 kJ4–41 Two tanks (Tank A and Tank B) are separated by apartition. Initially Tank A contains 2-kg steam at 1 MPa and300°C while Tank B contains 3-kg saturated liquid–vapormixture with a vapor mass fraction of 50 percent. Now thepartition is removed and the two sides are allowed to mixuntil the mechanical and thermal equilibrium are established.If the pressure at the final state is 300 kPa, determine (a) thetemperature and quality of the steam (if mixture) at the finalstate and (b) the amount of heat lost from the tanks.TANK A2 kg1 MPa300°CQFIGURE P4–41TANK B3 kg150°Cx = 0.510°CRadiatorRoomFIGURE P4–42Specific Heats, u, and h of Ideal Gases4–43C Is the relation u mc v,avg T restricted to constantvolumeprocesses only, or can it be used for any kind ofprocess of an ideal gas?4–44C Is the relation h mc p,avg T restricted to constantpressureprocesses only, or can it be used for any kind ofprocess of an ideal gas?4–45C Show that for an ideal gas c _ p c_ v R u .4–46C Is the energy required to heat air from 295 to 305 Kthe same as the energy required to heat it from 345 to 355 K?Assume the pressure remains constant in both cases.4–47C In the relation u mc v T, what is the correctunit of c v — kJ/kg · °C or kJ/kg · K?4–48C A fixed mass of an ideal gas is heated from 50 to80°C at a constant pressure of (a) 1 atm and (b) 3 atm. Forwhich case do you think the energy required will be greater?Why?4–49C A fixed mass of an ideal gas is heated from 50 to80°C at a constant volume of (a) 1 m 3 and (b) 3 m 3 . For whichcase do you think the energy required will be greater? Why?4–50C A fixed mass of an ideal gas is heated from 50 to80°C (a) at constant volume and (b) at constant pressure. Forwhich case do you think the energy required will be greater?Why?4–51 Determine the enthalpy change h of nitrogen, inkJ/kg, as it is heated from 600 to 1000 K, using (a) theempirical specific heat equation as a function of temperature(Table A–2c), (b) the c p value at the average temperatureQ